Improving constitutive equations in multiscale modelling by means of the sufficiency criterion using the example of nano wire contraction. Issue 1 (17th December 2018)

• Record Type: Journal Article
• Authors: Kurzeja, Patrick; Sievers, Christian; Mosler, Jörn
• Other Names: Müller G. guestEditor.; Ulbrich M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 18:Issue 1(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-12-17
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201800292
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: We demonstrate how two concepts from statistical modelling, namely the sufficiency criterion and the Rao‐Blackwell‐Kolmogorov theorem, can improve mechanical models. Applied to the contraction of relaxed nano wires, we start with a rough and simple equation. A set of sufficient parameters is then used to derive an improved equation that resembles the real solution in shape and quantity. The analytical solution and molecular simulations will finally highlight the functionality and the advantages of the scheme.